NxDWS - Calculates the Downside Deviation

Returns the downside deviation of a given data set.

Syntax

NxDWS([x],m)

[x]

is the portfolio simple rate of returns data series (a one-dimensional array of cells (e.g., rows or columns)).

m

is the minimum acceptable return (MAR). If missing, a zero (0) value is assumed.

Remarks

1. The downside deviation (DWS) measures downside risk and focuses on returns below a minimum threshold or acceptable return (MAR).
2. The DWS is an indicator used to assess the relative riskiness of one investment fund or strategy versus another.
3. By definition, all values in the input data set (i.e., X) must be greater than -1.0.
4. The input data series may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell) but will not be included in the calculations.
5. The DWS is computed as follows:
   
   $$\textrm{DWS}= \sqrt{\frac{\sum_{i=1}^{N}{G(r_i)}}{N}}$$
   $$G(r_i)=\left\{\begin{matrix} (r_i-r_m)^2 & r_i<r_m\\ 0 & ri \geqslant r_m \end{matrix}\right. $$
   Where:
   
   • $N$ is the number of data points with non-missing values.
   • $r_i$ is the simple return for the i-th data point.
   • $r_m$ is the minimum acceptable return (MAR).

Related Links

• Wikipedia - Downside risk
• Investopedia - Downside Deviation

References

• Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740